What are citations?
In SEO, a citation is simply an online reference to your business's name, address & phone number (NAP). They should include a link back to the appropriate URL where your office/location is, but that is not technically required to be a citation.
They look like this:
Why are citations important?
Citations help build the relevance, trust & authority of your business for search engines.
Like links to your website, Google uses citations when evaluating the online trust & authority of your business. However, citations do not have to be hyperlinked to your website in order for you to be credited for them (although you definitely should include a link, because that is just extra authority)
Where do citations occur?
Citations (or an instance of your NAP) are typically found on Directory Websites. However, they can be found on social media properties as well, or Web 2.0s, etc. Any website or page that has your NAP on it is technically a citation